Unlike Romney, Obama wants to make sure any tax reform produces a big new chunk of revenue to address the deficit. Yet it's difficult to do that and not hit the middle class. It's Romney's far more ambitious tax plan, however, that has become front and center in the presidential campaign.

Romney promises a 20 percent cut in tax rates, but he won't say which deductions he'll kill to pay for it. He promises a wholesale rewrite of the tax code that would cut income tax rates across the board, taking the top rate from 35 percent to 28 percent.

Romney's plan offers the dessert of sweeping tax cuts but not the vegetables of how he would pay for it. He and running mate Paul Ryan – his House GOP budget plan promises an even lower top tax rate of 25 percent – say they'll curb tax breaks and rely on fresh revenue from economic growth to recoup the cost.

Obama would instead raise that top rate to 39.6 percent, making clear he's still wedded to the idea that individuals with incomes above $200,000 and couples earning above $250,000 should pay more. It's never gotten anywhere on Capitol Hill, even when Democrats had sweeping House and Senate majorities in Obama's first two years in office.

Romney says he will eliminate taxes on inherited wealth and abolish taxes on capital gains and investment income for couples making less than $200,000 a year. He also would do away with the alternative minimum tax.

All of this, the Republican vows, will not reduce the share of taxes paid by wealthier people – nor raise taxes on the middle class or poor.

"I'm not going to raise taxes on anyone," he promised in his first debate with Obama.

Critics of Romney's plan say it simply doesn't add up. They say the estimated cost of the cuts – the $5 trillion over a decade figure tossed about on the campaign trail and in Obama's television ads – can't be recouped without slashing deductions and other tax breaks that chiefly benefit the middle- and upper middle-class.

Such popular – and entrenched – tax breaks include the deductions for home mortgage interest, charitable giving, and state and local taxes and the exclusion for employer-paid health insurance.

"You can't do all those things," said Roberton Williams of the Tax Policy Center, a Washington-based think tank. "The rich get such savings from the rate cuts that there just aren't enough tax breaks that benefit them that taking them away would recoup the full lost revenue from the rate cuts."

Such critics were given a boost on Friday when the nonpartisan tax analyst for Congress released a study that says eliminating all itemized deductions would pay for just a 4 percent cut in tax rates – far below Romney's 20 percent target.

Republicans pointed out that the Joint Committee on Taxation analysis was simply a sketchy outline of tax reform concepts and that there are very big differences between the panel's assumptions and the Romney plan. For starters, the congressional study started from a narrower set of tax breaks from which to finance the rate cuts.

However, wiping out every tax deduction – including those for mortgage interest, for state and local taxes and for charitable giving, but leaving breaks for health insurance and retirement savings or the personal exemption alone – would raise $2.5 trillion over a decade, just about half of the cost of Romney's plan.

Romney's plan to swap a $5 trillion slice of revenue over a decade from rate cuts while gleaning an equally big slice of revenue by curbing deductions and other tax breaks faces enormous, perhaps insurmountable challenges. The estimate comes from the Tax Policy Center, a think tank that's a joint project of the Brookings Institution and the Urban Institute.

The nonpartisan think tank recently rattled the debate with a study that estimated that Romney's plan would require slashing middle-class tax breaks so deeply that a family making between $75,000 and $100,000 could have to pay an average $2,000 more.

The Romney campaign disputes the math and the methodology and insists it's possible to do. Romney himself has tossed out hints that he might cap taxpayer deductions at, say, $17,000, $25,000 or $50,000. A campaign aide said he's considering curbing personal exemptions and the tax exclusion of employer-paid health insurance, particularly for those with higher incomes.

But without specifics it's impossible to analyze who would pay more and who would pay less. For families with children, a big mortgage, and who live in high tax states, for instance, might face a tax increase, while people who've paid off their houses and live in low tax states would see a tax cut.

Obama's core promise on taxes is what it's always been: Renew the tax cuts passed during George W. Bush's tenure, except for individuals whose income exceeds $200,000 and for married couples exceeds $250,000. That would raise the top income tax rate from 35 percent to 39.6 percent, back where it was during the Clinton era.

Obama also recommends limiting itemized deductions for such higher earners, phasing out their personal exemptions and increasing their rate on capital gains from 15 to 20 percent.

But Obama has never fought hard for the official tax plan that's in his budget, though he vows to hold the line and increase taxes on the wealthy if re-elected.

Instead, Obama hints he could support comprehensive tax reform like he did in negotiations with GOP House Speaker John Boehner of Ohio last summer. The Democratic platform says he's "committed to reforming our tax code so that it is fairer and simpler" and also guarantees that "no millionaire pays a smaller share of his or her income in taxes than middle class-families do."

It's commonly believed in Washington that the only way Republicans could ever vote for higher revenues – no easy assumption – is as part of a tax reform plan that lowers all rates, sharply curbs tax breaks and skims some of the revenue to defray the deficit.

Some Democrats, like Sen. Chuck Schumer of New York, say it's impossible to do all three without hitting the middle class.